Related papers: A representation basis for the quantum integrable …
We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2,2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard…
We derive spin operator matrix elements between general eigenstates of the superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by R.Baxter. For each…
We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of SU($N$), where $N$ is the dimension of the local Hilbert space. This approach, that generalizes the well-known Landau-Lifshitz dynamics from…
Using a technique based on the Yangian Gelfand-Zetlin algebra and the associated Yangian Gelfand-Zetlin bases we construct an orthogonal basis of eigenvectors in the Calogero-Sutherland Model with spin, and derive product-type formulas for…
We construct the Hilbert space costratification of $G=\mathrm{SU}(2)$-quantum gauge theory on a finite spatial lattice in the Hamiltonian approach. We build on previous work where we have implemented the classical gauge orbit strata on…
We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a…
An algebra homomorphism $\psi$ from the nonstandard q-deformed (cyclically symmetric) algebra $U_q(so_3)$ to the extension ${\hat U}_q(sl_2)$ of the Hopf algebra $U_q(sl_2)$ is constructed. Not all irreducible representations of $U_q(sl_2)$…
We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a…
In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space $H$ to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in…
The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux…
We study the symmetry properties of the single-band Hubbard model with general spin-orbit coupling (SOC) on the Kagome lattice. We show that the global U(1) spin-rotational symmetry is present in the Hubbard Hamiltonian owing to the…
The integrable quantum models, associated to the transfer matrices of the 6-vertex reflection algebra for spin 1/2 representations, are studied in this paper. In the framework of Sklyanin's quantum separation of variables (SOV), we provide…
In this paper we consider the simplified form that a recently introduced general operator description of the Hubbard model on the square lattice with $N_a^2\gg 1$ sites, effective transfer integral $t$, and onsite repulsion $U$ has in a…
We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the…
The open spin $s$ XXZ model with non-diagonal boundaries is considered. Within the algebraic Bethe ansatz framework and in the spirit of earlier works we derive suitable reference states. The derivation of the reference state is the crucial…
We define a 3-generator algebra obtained by replacing the commutators by anticommutators in the defining relations of the angular momentum algebra. We show that integer spin representations are in one to one correspondence with those of the…
With the XXZ spin chains as examples, we prove two theorems: (1) the functional relations derived from the off-diagonal Bethe Ansatz scheme are the sufficient and necessary conditions to characterize the complete spectrum of the…
We construct a three-dimensional superconformal quantum mechanics (and its associated de Alfaro-Fubini-Furlan deformed oscillator) possessing an $sl(2|1)$ dynamical symmetry. At a coupling parameter $\beta\neq 0$ the Hamiltonian contains a…
An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is proposed, based on the pseudo-SU(3) model. The Hamiltonian and the spectroscopic factor operator of the model are presented and a procedure of constructing the model…
We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions,…